Ecological Archives E084-073-A1

Michael H. Graham. 2003. Confronting multicollinearity in ecological multiple regression. Ecology 84:2809–2815.

Appendix A. SYSTAT output for backwards stepwise multiple regression. Response = depth of giant kelp shallow limit (in meters); OD = wave orbital displacement (in meters); BD = wave breaking depth (in meters); LTD = average tidal height (in meters); W = wind velocity (in meters/s). Backwards stepwise multiple regression was run using MGLH:REGRESSION under the STATS menu in SYSTAT 5.2 for Macintosh. Response was the dependent variable; CONSTANT, OD, BD, LTD, and W were the dependent variables; Stepwise was set to custom, with a backwards step order, and P = 0.15 to remove. Only standard SYSTAT output is presented.

Backwards stepwise variable selection
   
DEPENDENT VARIABLE: RESPONSE  
   

MINIMUM TOLERANCE FOR ENTRY INTO MODEL =  0.010000

 

 

Initial model
             
STEP #0;  R= 0.775; RSQUARE=  0.601            
             
IN            
             
---            
             
VARIABLE 
COEFF
SE 
STD COEF
TOLER
F
P
             
1 CONST            
             
2 OD
0.1433 
0.046 
0.55
 0.38836 
 9.57 
 0.0040 
             
3 BD
-0.0042
0.021
-0.03
0.42462
0.04
0.8402
             
4 LTD
-0.0596
0.142
-0.05
0.85087
0.17
0.6791
             
5 W
0.0079
0.004 
0.30
0.47748
3.57
0.0677
             
OUT PART. CORR          
             
---            
             

none

           
             

 

1st variable removal
             
STEP #1;  R= 0.775; RSQUARE=  0.600            
             
TERM REMOVED: BD            
             
IN            
             
---            
             
VARIABLE
COEFF
SE
STD COEF
TOLER
F
P
             
1 CONST            
             
2 OD
0.1384
0.038
0.53
0.53399
13.0
0.0011
             
4 LTD
-0.0553
0.139
-0.05
0.87021
0.16
0.6938
             
5 W
0.0077
0.004
0.29
0.50605
3.69
0.0629
             
OUT 
PART. CORR
         
             
---            
             
3 BD
-0.035
N/A
N/A
0.42462
0.04
0.8402
             

 

2nd variable removal
             
STEP #2;  R= 0.773; RSQUARE=  0.598            
             
TERM REMOVED: LTD            
             
IN            
             
---            
             
VARIABLE
COEFF
SE 
STD COEF
TOLER
F
P
             
1 CONST            
             
2 OD
0.1392 
0.038
0.53
0.53564
13.0
0.0009
             
5 W 
0.0081
0.004
0.31
0.53564
4.41
0.0431
             
OUT PART. CORR          
             
---            
             
3 BD
-0.025
N/A
N/A 
0.43420
0.02
0.8861
             
4 LTD
-0.068
N/A 
N/A 
0.87021
0.16
0.6938
             

 

THE SUBSET MODEL INCLUDES THE FOLLOWING PREDICTORS:
             
CONSTANT            
             
D            
             
W            
             
             
Parameterization of final model
             
DEP VAR: RESPONSE   N: 38; MULTIPLE R: 0.773; SQUARED MULTIPLE R: 0.598; ADJUSTED SQUARED MULTIPLE R: 0.575;STANDARD ERROR OF ESTIMATE: 0.139
             
VARIABLE
COEFF
SE
STD COEF
TOLER
F
P
             
CONST
2.873
0.097
0.00
N/A
30.0
0.0000
             
OD
0.139
0.038
0.53
0.53564
3.62
0.0009
             
W
0.008
0.004
0.31
0.53564
2.10
0.0431
             
Analysis of variance
             
SOURCE
SS
DF
MS
P
 
 
 
REGRESSION
1.012
0.51
26.06
0.0000
 
             
RESIDUAL
0.679
35
0.02
     
             


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